Particular patterning methods are used for fabricating large scale integrated electrical circuits with small structure dimensions. One of the most familiar methods known since the beginnings of semiconductor technology is the lithographic patterning method. In this case a radiation-sensitive resist or photoresist layer is applied to the surface of a semiconductor substrate wafer to be patterned and is exposed with the aid of electromagnetic radiation through a lithography mask. In the exposure operation, mask structures of the layout of the lithography mask are imaged onto the photoresist layer with the aid of a lens or a lens system and transferred into the photoresist layer by means of a subsequent development process. The photoresist structures fabricated in this way are subsequently used as an etching mask in the formation of the structures in the surface of the semiconductor substrate wafer in one or more etching processes.
A principal aim of the lithographic patterning method consists in a very precise transfer of a mask layout onto the surface of a semiconductor substrate wafer. However, optical errors and process errors give rise to distortions of the imaged mask layout on the semiconductor substrate wafer. Typical imaging distortions include, inter alia, a rounding of edges, a shortening of lines and nonuniform line widths. Distortions of this type, which occur especially in the case of very small mask structures having structure sizes smaller than the wavelengths of the electromagnetic radiation used, consequently reduce the achievable resolution limit of the mask structures.
In order to increase the resolution limit in the fabrication of small structures on semiconductor substrate wafers, special methods referred to as “resolution enhancement techniques” are used. One of these techniques is that of “optical proximity correction” (OPC), in which the mask structures of a lithography mask are drawn in modified fashion in such a way that undesirable imaging distortions are compensated for or minimized. In this case, a distinction is made between so-called rule-based optical proximity correction (“rule-based OPC”) and so-called model-based optical proximity correction (“model-based OPC”).
In rule-based proximity correction, the mask structures are classified into different classes depending on their geometry or structure size and a predetermined correction is assigned to each structure class. In this way, corrections to a mask layout of a lithography mask can indeed be performed relatively rapidly. However, one disadvantage is that corrections of this type are inaccurate particularly in the case of very small structures and, as a result, imaging distortions may possibly be compensated for only inadequately.
In contrast to this, in a model-based optical proximity correction, the corrections to a mask layout are carried out with the aid of computer simulations that use different models, generally an optical model and a resist model. The optical model is used to simulate illumination settings of the radiation source emitting the electromagnetic radiation and imaging properties of the lens system. The exposure and development properties of the photoresist layer are registered by means of the resist model. In comparison with a rule-based proximity correction, a model-based proximity correction requires a higher expenditure of time, but more precise corrections to a mask layout can be carried out. Known embodiments of a model-based optical proximity correction are disclosed for example in WO 00/67074 A1 and Nicolas Cobb, “Fast optical and process proximity correction algorithms for integrated circuit manufacturing”, PhD Thesis, University of California, Berkeley, 1998.
A model-based optical proximity correction comprises the substeps of optical modeling, resist modeling and the actual correction run, in which sections of a mask layout are successively optimized iteratively to a specific target dimension in the image. In optical modeling, which is essentially based on the imaging algorithm disclosed in H. H. Hopkins “On the diffraction theory of optical images”, in Proceedings of the royal society of London, Series A, Volume 217, No. 1131, pages 408-432, 1953, a four-dimensional matrix of transmission cross coefficients is calculated by multiple evaluation of an integral incorporating the product of an illumination aperture, a lens aperture and a complex conjugate lens aperture. In this case, optical properties of a lens system are reproduced by means of the lens aperture and illumination settings are reproduced by means of the illumination aperture. The matrix of transmission cross coefficients, which is used in the later correction run for different layout sections is usually additionally subjected to a singular value decomposition.
For the case of simple geometries of the illumination and lens apertures, it is possible to evaluate the integral for determining the transmission cross coefficients analytically and thus relatively rapidly. However, if the apertures are given as “bitmaps” or image matrices which enable a more complex and precise description of the underlying lens system and the illumination settings, then the evaluation takes substantially longer depending on the desired accuracy or the size of the raster of the image matrices. Consequently, an optical modeling carried out with a high accuracy requires a very high expenditure of time. This expenditure of time can only be reduced by reducing the accuracy of the modeling and thus of the later correction run.